Compute the waterplane area at a given draft using coefficients or numerical integration of station breadths.
AWP = — m²
AWP = — m²
Waterplane area is the horizontal area enclosed by a ship's hull at a stated waterline. It represents the plan shape formed where the immersed hull meets the water surface.
AWP is a hydrostatic property of one particular loading condition. It changes when the draft, trim or heel changes because the waterline may intersect a different part of the bow, stern and side geometry.
This calculator determines waterplane area either from the waterplane coefficient and principal waterline dimensions or by integrating breadths measured at equally spaced stations.
When the waterplane coefficient is known, the area is calculated from:
AWP = CWP × LWL × BWL
| Symbol | Meaning | Usual unit |
|---|---|---|
| AWP | Area enclosed by the selected waterline | m2 |
| CWP | Waterplane area coefficient at the selected waterline | Dimensionless |
| LWL | Length of the selected waterline | m |
| BWL | Maximum breadth on the same waterline | m |
With length and breadth entered in metres, the resulting area is obtained in square metres. All three inputs must describe the same waterline.
Consider a vessel with:
LWL × BWL = 180 × 30 = 5,400 m2
AWP = 0.820 × 5,400 = 4,428 m2
The waterplane area at the stated waterline is 4,428 m2.
The direct and station methods calculate the same property from different types of input.
| Method | Main inputs | Suitable use |
|---|---|---|
| Direct coefficient method | CWP, LWL and BWL | Known waterplane coefficient at the selected draft |
| Station integration | LWL and equally spaced full breadths or half-breadths | Waterline offsets or measured station ordinates |
Use the direct tab when CWP is known from hydrostatic data, a hull model or an earlier calculation.
The coefficient is itself defined as:
CWP = AWP ÷ (LWL × BWL)
The calculator rearranges this expression to obtain AWP. LWL should not be replaced by LPP or LOA unless the coefficient was specifically established with that alternative reference.
When waterline offsets are available, the area can be estimated by integrating breadths measured at equally spaced stations along LWL.
With N stations, the number of intervals is N − 1 and the station spacing is:
h = LWL ÷ (N − 1)
Simpson's one-third rule then gives:
AWP ≈ h ÷ 3 × [B0 + Bn + 4(B1 + B3 + ... + Bn−1) + 2(B2 + B4 + ... + Bn−2)]
B0 to Bn are full waterplane breadths. When half-breadth mode is selected, the calculator doubles each entered ordinate before applying the integration.
Station-count requirement: Simpson's one-third rule requires an even number of intervals and therefore an odd number of stations. The stations must also be equally spaced over the entered LWL.
Consider nine equally spaced stations over:
h = 180 ÷ (9 − 1) = 22.5 m
Odd-index breadths:
8.2 + 18.9 + 18.9 + 8.2 = 54.2 m
Even-index interior breadths:
14.6 + 20.0 + 14.6 = 49.2 m
AWP = 22.5 ÷ 3 × [0 + 0 + 4(54.2) + 2(49.2)]
AWP = 2,364 m2
The integrated waterplane area for the entered breadth series is 2,364 m2.
A full breadth is the complete transverse width of the waterplane at a station. A half-breadth is the distance from the centreline to one side of the waterplane.
Bi = 2yi
Select full-breadth mode when the entered values already represent the complete port-to-starboard width. Select half-breadth mode only when the values run from the centreline to one side.
Avoid double conversion: entering full breadths while half-breadth mode is selected doubles the area. Entering half-breadths in full-breadth mode gives approximately half the intended area for a symmetric waterplane.
CWP expresses the waterplane area as a proportion of its surrounding LWL × BWL rectangle. AWP is the actual area in square units.
Waterplane area is also related to tonnes per centimetre immersion:
TPC = ρ × AWP ÷ 100
When ρ is in t/m3 and AWP is in m2, TPC is obtained in t/cm.
For the direct worked example:
TPC = 1.025 × 4,428 ÷ 100 = 45.387 t/cm
This value describes the approximate displacement change for a small parallel change of draft near the stated waterline.
AWP controls the local rate at which displacement changes with draft. A larger waterplane area produces a larger TPC at the same water density.
The way that area is distributed is also important. Transverse and longitudinal waterplane moments of inertia depend on the positions of the area elements relative to their reference axes, not only on the total area.
BMT = IT ÷ ∇
BML = IL ÷ ∇
Two waterplanes can have the same AWP but different IT, IL and longitudinal centres of flotation. Their initial-stability and trim characteristics may therefore differ.
Area is not inertia: AWP alone does not determine GM, moment to change trim or longitudinal centre of flotation. Those calculations require the location and distribution of the waterplane area.
Waterplane area is valid only for the waterline from which it was obtained. As draft increases, flare, transom immersion, bow shape and stern geometry may alter the waterplane area.
For a vessel with appreciable trim, the forward and aft intersections of the hull occur at different vertical levels. A calculation based only on one nominal mean-draft waterline may not represent the true trimmed waterplane.
Heel can also change the waterplane outline, particularly on vessels with flare, chines, deck-edge immersion or asymmetric geometry.
Use waterline dimensions, coefficients and station breadths belonging to the same actual condition.
AWP is useful for determining TPC, checking hydrostatic data, comparing waterlines and supporting further stability and trim calculations.
Waterplane area alone cannot determine:
Result check: AWP must be positive and cannot exceed LWL × BWL when BWL is the maximum breadth of that waterline. An area above the reference rectangle normally indicates inconsistent inputs, duplicated half-breadths or incorrect dimensions.
The definitions and numerical relationships used on this page follow established naval architecture references:
NauticalSolver calculators are intended for preliminary engineering, study and independent checking. Use approved hydrostatic particulars and vessel-specific geometry for operational, contractual or statutory work.